A143724 Triangle read by rows, inverse Möbius transform of a diagonalized matrix of A116477.

1, 1, 2, 1, 0, 4, 1, 2, 0, 5, 1, 0, 0, 0, 9, 1, 2, 4, 0, 0, 7, 1, 0, 0, 0, 0, 0, 15, 1, 2, 0, 5, 0, 0, 0, 12, 1, 0, 4, 0, 0, 0, 0, 0, 18, 1, 2, 0, 0, 9, 0, 0, 0, 0, 15, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 1, 2, 4, 5, 0, 7, 0, 0, 0, 0, 0, 16

Offset

1,3

Comments

For n-th row of the triangle, the inverse Möbius transform extracts A116477(k) such that k divides n; 0 otherwise.

Row sums = A006218: (1, 3, 5, 8, 10, 14, 16, ...).

Links

Table of n, a(n) for n=1..78.

Formula

Triangle read by rows, A051731 * (A116477 * 0^(n-k)); 1 <= k <= n.

Example

First few rows of the triangle:
1;
1, 2;
1, 0, 4;
1, 2, 0, 5;
1, 0, 0, 0, 9;
1, 2, 4, 0, 0, 7;
1, 0, 0, 0, 0, 0, 15;
1, 2, 0, 5, 0, 0,  0, 12;
...
Example: The divisors of 8 are (1, 2, 4, 8) so row 8 = (1, 2, 0, 5, 0, 0, 0, 12).

Crossrefs

Cf. A006218, A051731, A116477.

Sequence in context: A326759 A140882 A334044 * A143425 A323376 A166555

Adjacent sequences: A143721 A143722 A143723 * A143725 A143726 A143727

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 29 2008

Extensions

Diagonal sequence corrected to A116477 by Georg Fischer, Jun 27 2023

Status

approved